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Hybridizing gravitational search algorithm with real coded genetic algorithms for structural engineering design problem

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Abstract

The focus of this paper is gravitational search algorithm which is a relatively new heuristics algorithm for function optimization. In order to improve the efficiency and reliability it was hybridized with real coded genetic algorithm and extensively applied to solve benchmarks problems available in literature. In the present paper, these hybridized variants are used to solve three constrained engineering design problem. The obtained results are compared with an extensively available results in literature. It is proved that the performance of one of the hybridized version outperform the remaining hybridized version as well as original gravitational search algorithm, in term of quality of solution and computation effort.

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References

  1. Lee, K.S., Geem, Z.W.: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput. Methods Appl. Mech. Eng. 194(36), 3902–3933 (2005)

    Article  Google Scholar 

  2. Liu, J., Wu, C., Wu, G., Wang, X.: A novel differential search algorithm and applications for structure design. Appl. Math. Comput. 268, 246–269 (2015)

    Google Scholar 

  3. Liu, J., Teo, K.L., Wang, X., Wu, C.: An exact penalty function-based differential search algorithm for constrained global optimization. Soft Comput. 20(4), 1305–1313 (2016)

    Article  Google Scholar 

  4. Canayaz, M., Karci, A.: Cricket behaviour-based evolutionary computation technique in solving engineering optimization problems. Appl. Intell. 44(2), 362–376 (2016)

    Article  Google Scholar 

  5. Cuevas, E., Cienfuegos, M.: A new algorithm inspired in the behavior of the social-spider for constrained optimization. Expert Syst. Appl. 41(2), 412–425 (2014)

    Article  Google Scholar 

  6. Coello, C.A.C.: Use of a self-adaptive penalty approach for engineering optimization problems. Comput. Ind. 41(2), 113–127 (2000)

    Article  Google Scholar 

  7. Deb, K.: Optimal design of a welded beam via genetic algorithms. AIAA J 29(11), 2013–2015 (1991)

    Article  Google Scholar 

  8. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2), 311–338 (2000)

    Article  Google Scholar 

  9. Deb, K.: GeneAS: a robust optimal design technique for mechanical component design. In: Dasgupta, D., Michalewicz, Z. (eds.) Evolutionary Algorithms in Engineering Applications, pp. 497–514. Springer, Berlin (1997)

    Chapter  Google Scholar 

  10. Dimopoulos, G.G.: Mixed-variable engineering optimization based on evolutionary and social metaphors. Comput. Methods Appl. Mech. Eng. 196, 803–817 (2007)

    Article  Google Scholar 

  11. He, Q., Wang, L.: An effective co-evolutionary particle swarm optimization for con-strained engineering design problems. Eng. Appl. Artif. Intell. 20, 89–99 (2007)

    Article  Google Scholar 

  12. He, S., Prempain, E., Wu, Q.H.: An improved particle swarm optimizer for mechanical design optimization problems. Eng. Optim. 36(5), 585–605 (2004)

    Article  Google Scholar 

  13. Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, pp. 69–73. IEEE Press, Piscataway (1998)

  14. Cagnina, L.C., Esquivel, S.C., Coello, C.A.C.: Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32, 319–326 (2008)

    Google Scholar 

  15. Mahdavi, M., Fesanghary, M., Damangir, E.: An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput. 188, 1567–1579 (2007)

    Google Scholar 

  16. Fesanghary, M., Mahdavi, M., Minary-Jolandan, M., Alizadeh, Y.: Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. Comput. Methods Appl. Mech. Eng. 197, 3080–3091 (2008)

    Article  Google Scholar 

  17. Garg, H.: Solving structural engineering design optimization problems using an artificial bee colony algorithm. J. Ind. Manag. Optim. 10(3), 777–794 (2014)

    Article  Google Scholar 

  18. Gandomi, A.H., Yang, X.S., Alavi, A.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29, 17–35 (2003)

    Article  Google Scholar 

  19. Yang, X.S., Deb, S.: Engineering optimisation by cuckoo search. Int. J. Math. Model. Numer. Optim. 1(4), 330–343 (2010)

    Google Scholar 

  20. Hwang, S.F., He, R.S.: A hybrid real-parameter genetic algorithm for function optimization. Adv. Eng. Inf. 20(1), 7–21 (2006)

    Article  Google Scholar 

  21. Kaveh, A., Talatahari, S.: An improved ant colony optimization for constrained engineering design problems. Eng. Comput. 27, 155–182 (2010)

    Article  Google Scholar 

  22. Kaveh, A., Talatahari, S.: Engineering optimization with hybrid particle swarm and ant colony optimization. Asian J. Civ. Eng. (Build. Hous.) 10, 611–628 (2009)

    Google Scholar 

  23. Hedar, A.R., Fukushima, M.: Derivative-free filter simulated annealing method for con-strained continuous global optimization. J. Glob. Optim. 35, 521–549 (2006)

    Article  Google Scholar 

  24. Coello, C.A.C., Montes, E.M.: Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv. Eng. Inform. 16, 193–203 (2002)

    Article  Google Scholar 

  25. Mezura-Montes, E., Coello, C.A.C., Velázquez-Reyes, J., Muñoz-Dávila, L.: Multiple trial vectors in differential evolution for engineering design. Eng. Optim. 39(5), 567–589 (2007)

    Article  Google Scholar 

  26. Liu, H., Cai, Z., Wang, Y.: Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl. Soft Comput. 10(2), 629–640 (2010)

    Article  Google Scholar 

  27. Ragsdell, K.M., Phillips, D.T.: Optimal design of a class of welded structures using geometric programming. ASME J. Eng. Ind. 98, 1021–1025 (1976)

    Article  Google Scholar 

  28. Mehta, V.K., Dasgupta, B.: A constrained optimization algorithm based on the simplex search method. Eng. Optim. 44(5), 537–550 (2012)

    Article  Google Scholar 

  29. Gandomi, A.H., Yang, X.S., Alavi, A.H.: Mixed variable structural optimization using firefly algorithm. Comput. Struct. 89, 2325–2336 (2011)

    Article  Google Scholar 

  30. Zhang, C., Wang, H.P.: Mixed-discrete nonlinear optimization with simulated annealing. Eng. Optim. 21, 277–291 (1993)

    Article  Google Scholar 

  31. Ao, Y.Y., Chi, H.Q.: An adaptive differential evolution algorithm to solve constrained optimization problems in engineering design. Engineering 2(01), 65–77 (2010)

    Article  Google Scholar 

  32. Zhang, M., Luo, W., Wang, X.: Differential evolution with dynamic stochastic selection for constrained optimization. Inf. Sci. 178, 3043–3074 (2008)

    Article  Google Scholar 

  33. Omran, M.G.H., Salman, A.: Constrained optimization using CODEQ. Chaos Solitons Fractals 42, 662–668 (2009)

    Article  Google Scholar 

  34. Coelho, L.S.: Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst. Appl. 37, 1676–1683 (2010)

    Article  Google Scholar 

  35. He, S., Prempain, E., Wu, Q.H.: An improved particle swarm optimizer for mechanical design optimization problems. Eng. Optim. 36, 585–605 (2004)

    Article  Google Scholar 

  36. Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)

    Article  Google Scholar 

  37. Sabri, N.M., Puteh, M., Mahmood, M.R.: A review of gravitational search algorithm. Int. J. Adv. Soft Comput. 5(3), 1–39 (2013)

    Google Scholar 

  38. Singh, A., Deep, K.: Real Coded Genetic Algorithm Operators Embedded in Gravitational Search Algorithm for Continuous Optimization. Int. J. Intell. Syst. Appl. 7(12), 1–22 (2015)

    Google Scholar 

  39. Singh, A., Deep, K.: Novel hybridized variants of gravitational search algorithm for constraint optimization. Int. J. Swarm Intell. (in press)

  40. Deep, K., Thakur, M.: A new crossover operator for real coded genetic algorithms. Appl. Math. Comput. 188(1), 895–911 (2007)

    Google Scholar 

  41. Deep, K., Thakur, M.: A new mutation operator for real coded genetic algorithms. Appl. Math. Comput. 193(1), 211–230 (2007)

    Google Scholar 

  42. Rao, S.S., Rao, S.S.: Engineering Optimization: Theory and Practice. Wiley, Hoboken, New Jersey (2009)

    Book  Google Scholar 

  43. Kannan, B.K., Kramer, S.N.: An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Trans. ASME J. Mech. Des. 116, 405–411 (1994)

    Article  Google Scholar 

  44. Ray, T., Liew, K.M.: Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans. Evol. Comput. 7(4), 386–396 (2003)

    Article  Google Scholar 

  45. Hu, X.H., Eberhart, R.C., Shi, Y.H.: Engineering optimization with particle swarm. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, pp. 53–57 (2003)

  46. Montes, E.M., Coello, C.A.C., Reyes, J.V., Davila, L.M.: Multiple trial vectors in differential evolution for engineering design. Eng. Optim. 39, 567–589 (2007)

    Article  Google Scholar 

  47. Montes, E.M., Coello, C.A.C.: An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int. J. Gen. Syst. 37, 443–473 (2008)

    Article  Google Scholar 

  48. Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical report, TR06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)

  49. Sandgren, E.: Nonlinear integer and discrete programming in mechanical design. In: Proceedings of the ASME Design Technology Conference, pp. 95–105. F.L. Kissimine (1988)

  50. Belegundu, A.D.: A study of mathematical programming methods for structural optimization. PhD thesis, Department of Civil and Environmental Engineering, University of Iowa, Iowa, USA (1982)

  51. Arora, J.S.: Introduction to Optimum Design. McGraw-Hill, New York (1989)

    Google Scholar 

  52. Ray, T., Saini, P.: Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng. Optim. 33, 735–748 (2001)

    Article  Google Scholar 

  53. Raj, K.H., Sharma, R.S., Mishra, G.S., Dua, A., Patvardhan, C.: An evolutionary computational technique for constrained optimisation in engineering design. J. Inst. Eng. India Part Me Mech. Eng. Div. 86, 121–128 (2005)

    Google Scholar 

  54. Tsai, J.: Global optimization of nonlinear fractional programming problems in engineering design. Eng. Optim. 37, 399–409 (2005)

    Article  Google Scholar 

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Acknowledgements

Amarjeet Singh would like to thank Council for Scientific and Industrial Research (CSIR), New Delhi, India, for providing him the financial support vide Grant Number 09/143(0824)/2012-EMR-I.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Amarjeet Singh & Kusum Deep

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  1. Amarjeet Singh
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Correspondence to Amarjeet Singh.

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Singh, A., Deep, K. Hybridizing gravitational search algorithm with real coded genetic algorithms for structural engineering design problem. OPSEARCH 54, 505–536 (2017). https://doi.org/10.1007/s12597-016-0291-4

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